Abstract
We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand–Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand–Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.
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08 April 2021
A Correction to this paper has been published: https://doi.org/10.1007/s00041-021-09824-3
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Communicated by Michael Ruzhansky.
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Carypis, E., Wahlberg, P. Propagation of Exponential Phase Space Singularities for Schrödinger Equations with Quadratic Hamiltonians. J Fourier Anal Appl 23, 530–571 (2017). https://doi.org/10.1007/s00041-016-9478-6
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DOI: https://doi.org/10.1007/s00041-016-9478-6
Keywords
- Schrödinger equation
- Heat equation
- Propagation of singularities
- Phase space singularities
- Gelfand–Shilov wave front set